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Laser physics EAL 501 Lecture 3 Energy units • 1 eV= 1.6x10-19 (C) x 1 V= 1.6x10-19 J • E =hc/λ • 1/λ=E/hc=1J/(6.6x10-34x108x100) 1 cm-1 =1.5 x10-23 J =.00012 eV Absorption, Emission, and Dispersion of Light • Electron Oscillator Model • Spontaneous Emission • Absorption • Thermal Radiation • Emission and Absorption of Narrowband Light • Collision Broadening • Doppler Broadening • The Voigt Profile • Radiative Broadening • Absorption and Gain Coefficients Absorption of gases • White light propagating through a gas is absorbed at the resonance frequencies of the atoms or molecules. Sodium, for instance, has strong absorption lines in the yellow region at 589.0 and 589.6 nm The absorbed energy is dissipated in • Heat (translational kinetic energy of the atoms) • Collision • Resonance fluorescence :Re-emission in all directions ( • Radiation quenching :When the pressure of the gas is increased, collisions may rapidly convert the absorbed radiation into heat before it can be reradiated. Lorentz model • This hypothesis states that an electron in an atom responds to light as if it were bound to its atom or molecule by a simple spring. As a consequence the electron can be imagined to oscillate about the nucleus. F x kx Fv .v 2 F m. d x dt 2 e . E kx dx 2 m dt 2 d x dt 2 dx m dt d x dt k m 2 x e . E cos( t ) Fe eE ( x , t ) Electron Natural oscillation: Solution if no external field and no friction 2 d x 2 k x x A cos( o t ) o k dt m m This corresponds to the spontaneous emission In the presence of External field , the electron can absorb energy only if ω= ωo The friction correspond to radiation losses in the material. Semi classical view spontaneous emission Boltzman Law N 2 / N1 e E2 , N2 E 2 E1 k BT E1 , N1 d dt N1 d dt N 2 A 21 N 2 A21 is the rate of spontaneous emission = 1/ τ21 the level 2 life time Or Decay time of level 2 to level 1 N 2 (t ) N 2 ( 0 ) e For multi level decay An A m t 21 nm Some forms of spontaneous emission • Electroluminescence : If excitation occurs in an electric discharge such as a spark. • Chemiluminescence : If excitation produced as a by-product of a chemical reaction. • Bioluminescence : If excitation occurs in a living organism (such as a firefly),. • Fluorescence refers to spontaneous emission from an excited state produced by the absorption of light. • Phosphorescence describes the situation in which the emission persists long after the exciting light is turned off and is associated with a metastable Absorption E2 , N2 d dt N 1 B12 N 1 I ( ) S ( ) S is the line shape The simplest is the Lorentzian line shape L L ( ) o / ( v o ) o 2 2 E1 , N1 Spectral energy density of radiation It is convenient to define a spectral energy density ρ(ν), such that ρ(ν) d ν is the electromagnetic energy per unit volume in the frequency band ν , ν+dν The intensity, or energy flux, is the velocity of light times the energy density. Therefore I(ν)dν = cρ(ν) Stimulated emission E2 , N2 E1 , N1 d dt N 2 B 21 N 2 I ( ) Thermal Radiation • A black body is a body that absorbs all the energy incident 8 h / c 3 ( ) h e max 3 k BT 2898 T 1 [ m ] Einstein relations g 2 B12 g 1 B 21 B 21 c 3 8 g 2 h 3 A 21 So for a two level system in the presence of radiation we can write d dt N2 d dt N 1 B12 ( ) S ( ) N 1 B 21 ( ) S ( ) N 2 A 21 N 1 B12 ( ) S ( )( N 1 g1 g2 N 2 ) A 21 N 1 Line shapes Natural line brodening : due to spontaneous emission Lorentzian line shape rad A nm / 4 Homogeneous line broadening : due to atomic collisions broadening increase with pressure o collisionr ate / 2 Inhomogeneous line broadening : due to Doppler effect Gaussian line shape Propagation of light through a 2 level medium Suppose a light of intensity Iv(0) is incident on the material. The intensity In is equal to the energy density per unit volume times the wave propagation velocity. The rate at which electromagnetic energy passes through a plane cross-sectional area A at z is Iv(z)A, and at an adjacent plane at z+dz this rate is Iv(z+dz)A; the difference is ( I ( z z ) I ( z )) A ( I v ( z ) A ) dz z The rate at which energy is accumulated or depleted in the volume Δz is t ( u ( ) A z ) z ( I ( z ) A ) z The change in radiation in the medium could be due to absorption and emission. If we neglect the spontaneous emission for the time being The rate of increase of N2 equals the rate of decrease of the field so ( ( ( 1 c t 1 c t 1 c t z z z ) I h B 21 u ( ) S ( )( N 2 ) I h B 21 S ( ) c ) I g ( ) I . (N 2 g2 g1 g2 g1 N1) N 1 ) I . The gain coefficient has dimension m-1 . If g >0 it is amplification. If g<0 it is absorption A21 2 g ( ) 8 S ( )( N 2 g2 g1 N1) Remember that the wave length here λ is the wave length inside the material which equals the wavelength in vacuum divided by the index of refraction of the material (the frequency doesn’t change inside the material A21 2 g ( ) 8 n 2 S ( )( N 2 g2 g1 N1)